> > Of course this reduces to the problem of "The Theory of Dust", and
> > we are right back to wondering how a pattern found in one cubic
> > lightyear of dust, that appears to be Sa, could really be connected
> > in any meaningful way with another pattern found in another cubic
> > lightyear 10,000,000 parsecs away. Again, I just don't think that
> > all those patches of dust constitute consciousness (no information
> > flow, no time involved). A perfectly consistent position for a
> > time chauvinist like me.
>
> Yes, it comes back to the same thing. I know I'm in a minority, but I don't
> see a problem with assuming that consciousness can happen with a succession
> of frozen states. The two reasons you give in your article for rejecting a
> conscious SFS are (a) that it's obviously absurd, and (b) that it doesn't
> result in information flow between the states. But I don't think it's
> obviously absurd, and I see the lack of information flow (or inability to
> handle counterfactuals) as just making it impossible for us as external
> observers to use the system for computation.

Since we're bringing in mathematical isomorphisms between systems (via
the hash function and the game of life), let's consider a simpler
example: differentiating functions. Let S be some finite (though
possibly very large) set of polynomial functions, closed under
differentiation. The derivative is a map from S to itself. Via a hash
function f, this is then seen as an abstract map from f(S) to itself.

Then what? Well, differentiation is connected with multiplication and
addition of functions. We can choose S to be sufficiently rich to have
many examples of this. Via f, we get some complicated relations on
f(S), and differentiation interacts with these relations (similaly,
localness can be phrased in terms of the image of the hash function;
it's just a lot more complicated).

So far, I see no reason to consider that S and f(S) should be treated
differently. Sure its more complicated in f(S), but consciousness is
complicated anyway.

I see only two ways of distinguishing S and f(S), and the equivalents
in the game of life: 1) The question asked and 2) The implicit
infinity.

1) The question asked.
When you ask "what is the derivative of this function", you are not
asking the equivalent (but hideously complicated) version in f(S). In
fact that hideously complicated question has no meaning unless we know
its simple equivalent. Similalrly, when we ask "what is
consciousness", we expect the answer to have meaning, while the hash
function equivalent is meaningless.

We can even formalise what we mean by meaning. "What is consciousness"
is a complicated question, but we know the outlines of the answer (and
it is not: the average wavelength of the light hitting Io during a
solar flare). The answer, whatever it is, will have simpler, quasi
answers - incomplete but informative. The has function equivalents
will not be simpler than the hash function equivalent to the full
question.

2) The implicit infinity.
Implicit in the definition of differentiation is the fact that we
could differentiate any polynomial (with, say, rational coefficients).
The definition of differentiation to f(S) does not extend to infinity
in this way; in fact, there is no evident extention of f(S).

So our definition of "differentiation" somehow covers an infinite
amount of cases, though it is defined finitely. A GLUT could not do
this.